The level of the 5PN corrections to Hamiltonian dynamics exhibits a complexity, which currently could only
be solved using the effective field theory approach. The latter has been originally developed for renormalizable
quantum field theories. There refined algorithms for the automated computer algebaric derivation of all dynamical
contributions and very efficient algorithms for term reduction exist [1]}, [2]}. Likewise, many methods
to compute the contributing integrals analytically have been developed [3]}. By these methods
the problem on hand could be solved. Any theory having a path integral representation, including classical
mechanics, can be formulated in this way. Here the path integral [4]} is a consequence of the variational
principles of mechanics [5]}, the basis of any dynamical physical law. Symbioses of different fields in
science
lead to progress in the present case. Future calculations will use similar technologies at higher post-Newtonian
orders. Given the fast growth of complexity, however, even more refined technologies have to be developed
to solve
these problems.
